Inelastic γ-ray scattering (Compton scattering) is a distinguished tool to explore the electronic and magnetic response of various substances and is also an emphatic technique to validate the quantum mechanical exchange and correlation potentials used in the DFT calculations. Charge and magnetic Compton profiles are used to deduce the electron/spin momentum densities in functional materials like dichalcogenides, ferrites, ferroelectrics, chromates, Heusler alloys, oxides, etc. In this review, besides salient features of basic principles of Compton scattering, we have included representative studies on Compton profiles and relative nature of bonding in lead titanate/lead zirconate. Temperature dependency of spin moments using magnetic Compton profiles of Pr doped NiFe2O4 system has also be discussed. Recent work on charge and magnetic Compton scattering of variety of materials is reviewed.